p^2+12p-54=0

Solution for p^2+12p-54=0 equation:

Simplifying
p2 + 12p + -54 = 0

Reorder the terms:
-54 + 12p + p2 = 0

Solving
-54 + 12p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '54' to each side of the equation.
-54 + 12p + 54 + p2 = 0 + 54

Reorder the terms:
-54 + 54 + 12p + p2 = 0 + 54

Combine like terms: -54 + 54 = 0
0 + 12p + p2 = 0 + 54
12p + p2 = 0 + 54

Combine like terms: 0 + 54 = 54
12p + p2 = 54

The p term is 12p.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12p + 36 + p2 = 54 + 36

Reorder the terms:
36 + 12p + p2 = 54 + 36

Combine like terms: 54 + 36 = 90
36 + 12p + p2 = 90

Factor a perfect square on the left side:
(p + 6)(p + 6) = 90

Calculate the square root of the right side: 9.486832981

Break this problem into two subproblems by setting 
(p + 6) equal to 9.486832981 and -9.486832981.

Subproblem 1
p + 6 = 9.486832981

Simplifying
p + 6 = 9.486832981

Reorder the terms:
6 + p = 9.486832981

Solving
6 + p = 9.486832981

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + p = 9.486832981 + -6

Combine like terms: 6 + -6 = 0
0 + p = 9.486832981 + -6
p = 9.486832981 + -6

Combine like terms: 9.486832981 + -6 = 3.486832981
p = 3.486832981

Simplifying
p = 3.486832981

Subproblem 2
p + 6 = -9.486832981

Simplifying
p + 6 = -9.486832981

Reorder the terms:
6 + p = -9.486832981

Solving
6 + p = -9.486832981

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + p = -9.486832981 + -6

Combine like terms: 6 + -6 = 0
0 + p = -9.486832981 + -6
p = -9.486832981 + -6

Combine like terms: -9.486832981 + -6 = -15.486832981
p = -15.486832981

Simplifying
p = -15.486832981

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {3.486832981, -15.486832981}